Energy-based stochastic control of neural mass models suggests time-varying effective connectivity in the resting state

Controlling neural activity: LPV modelling of optogenetically actuated Wilson-Cowan model. J Neural Eng 2024;21:036002. [PMID: 38653250 DOI: 10.1088/1741-2552/ad4212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Objective.This paper aims to bridge the gap between neurophysiology and automatic control methodologies by redefining the Wilson-Cowan (WC) model as a control-oriented linear parameter-varying (LPV) system. A novel approach is presented that allows for the application of a control strategy to modulate and track neural activity.Approach.The WC model is redefined as a control-oriented LPV system in this study. The LPV modelling framework is leveraged to design an LPV controller, which is used to regulate and manipulate neural dynamics.Main results.Promising outcomes, in understanding and controlling neural processes through the synergistic combination of control-oriented modelling and estimation, are obtained in this study. An LPV controller demonstrates to be effective in regulating neural activity.Significance.The presented methodology effectively induces neural patterns, taking into account optogenetic actuation. The combination of control strategies with neurophysiology provides valuable insights into neural dynamics. The proposed approach opens up new possibilities for using control techniques to study and influence brain functions, which can have key implications in neuroscience and medicine. By means of a model-based controller which accounts for non-linearities, noise and uncertainty, neural signals can be induced on brain structures.

Design of optimal nonlinear network controllers for Alzheimer's disease

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer’s disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients’ biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks–namely, networks having low average shortest path length, high global efficiency–are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

This work aims to close the knowledge gap between theory and experiment in brain stimulation. Previous modeling approaches for stimulation have overlooked the nonlinear dynamical nature of the brain and failed to shed light on efficient mechanisms for the exogenous control of the brain. Amid the current efforts for developing personalized medicine, we introduce a framework for producing tailored stimulation signals, based on individual neuroimaging data and innovative modeling. This is the first time, to our knowledge, that brain stimulation for the most common cause of dementia, Alzheimer’s disease, is theoretically addressed. Our approach leads to the identification of potential target regions and subjects to successfully respond to brain stimulation therapies and yields various disease-reverting signals. Although focused on Alzheimer’s in this study, our methodology could be applied to other clinical conditions characterized by abnormalities in brain dynamics, like epilepsy and Parkinson’s, the treatment of which can benefit from the use of optimal control strategies.

The Energy Landscape of Neurophysiological Activity Implicit in Brain Network Structure

A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of the brain. How does large-scale brain circuitry constrain states of neuronal activity and transitions between those states? We address these questions using a maximum entropy model of brain dynamics informed by white matter tractography. We demonstrate that the most probable brain states - characterized by minimal energy - display common activation profiles across brain areas: local spatially-contiguous sets of brain regions reminiscent of cognitive systems are co-activated frequently. The predicted activation rate of these systems is highly correlated with the observed activation rate measured in a separate resting state fMRI data set, validating the utility of the maximum entropy model in describing neurophysiological dynamics. This approach also offers a formal notion of the energy of activity within a system, and the energy of activity shared between systems. We observe that within- and between-system energies cleanly separate cognitive systems into distinct categories, optimized for differential contributions to integrated versus segregated function. These results support the notion that energetic and structural constraints circumscribe brain dynamics, offering insights into the roles that cognitive systems play in driving whole-brain activation patterns.

Temporal stability of network centrality in control and default mode networks: Specific associations with externalizing psychopathology in children and adolescents

Abnormal connectivity patterns have frequently been reported as involved in pathological mental states. However, most studies focus on "static," stationary patterns of connectivity, which may miss crucial biological information. Recent methodological advances have allowed the investigation of dynamic functional connectivity patterns that describe non-stationary properties of brain networks. Here, we introduce a novel graphical measure of dynamic connectivity, called time-varying eigenvector centrality (tv-EVC). In a sample 655 children and adolescents (7-15 years old) from the Brazilian "High Risk Cohort Study for Psychiatric Disorders" who were imaged using resting-state fMRI, we used this measure to investigate age effects in the temporal in control and default-mode networks (CN/DMN). Using support vector regression, we propose a network maturation index based on the temporal stability of tv-EVC. Moreover, we investigated whether the network maturation is associated with the overall presence of behavioral and emotional problems with the Child Behavior Checklist. As hypothesized, we found that the tv-EVC at each node of CN/DMN become more stable with increasing age (P < 0.001 for all nodes). In addition, the maturity index for this particular network is indeed associated with general psychopathology in children assessed by the total score of Child Behavior Checklist (P = 0.027). Moreover, immaturity of the network was mainly correlated with externalizing behavior dimensions. Taken together, these results suggest that changes in functional network dynamics during neurodevelopment may provide unique insights regarding pathophysiology.

Modeling the Generation of Phase-Amplitude Coupling in Cortical Circuits: From Detailed Networks to Neural Mass Models

Phase-amplitude coupling (PAC), the phenomenon where the amplitude of a high frequency oscillation is modulated by the phase of a lower frequency oscillation, is attracting an increasing interest in the neuroscience community due to its potential relevance for understanding healthy and pathological information processing in the brain. PAC is a diverse phenomenon, having been experimentally detected in at least ten combinations of rhythms: delta-theta, delta-alpha, delta-beta, delta-gamma, theta-alpha, theta-beta, theta-gamma, alpha-beta, alpha-gamma, and beta-gamma. However, a complete understanding of the biophysical mechanisms generating this diversity is lacking. Here we review computational models of PAC generation that range from detailed models of neuronal networks, where each cell is described by Hodgkin-Huxley-type equations, to neural mass models (NMMs) where only the average activities of neuronal populations are considered. We argue that NMMs are an appropriate mathematical framework (due to the small number of parameters and variables involved and the richness of the dynamics they can generate) to study the PAC phenomenon.

A switching multi-scale dynamical network model of EEG/MEG

We introduce a new generative model of the Encephalography (EEG/MEG) data, the inversion of which allows for inferring the locations and temporal evolution of the underlying sources as well as their dynamical interactions. The proposed Switching Mesostate Space Model (SMSM) builds on the multi-scale generative model for EEG/MEG by Daunizeau and Friston (2007). SMSM inherits the assumptions that (1) bioelectromagnetic activity is generated by a set of distributed sources, (2) the dynamics of these sources can be modelled as random fluctuations about a small number of mesostates, and (3) the number of mesostates engaged by a cognitive task is small. Additionally, four generalising assumptions are now included: (4) the mesostates interact according to a full Dynamical Causal Network (DCN) that can be estimated; (5) the dynamics of the mesostates can switch between multiple approximately linear operating regimes; (6) each operating regime remains stable over finite periods of time (temporal clusters); and (7) the total number of times the mesostates' dynamics can switch is small. The proposed model adds, therefore, a level of flexibility by accommodating complex brain processes that cannot be characterised by purely linear and stationary Gaussian dynamics. Importantly, the SMSM furnishes a new interpretation of the EEG/MEG data in which the source activity may have multiple discrete modes of behaviour, each with approximately linear dynamics. This is modelled by assuming that the connection strengths of the underlying mesoscopic DCN are time-dependent but piecewise constant, i.e. they can undergo discrete changes over time. A Variational Bayes inversion scheme is derived to estimate all the parameters of the model by maximising a (Negative Free Energy) lower bound on the model evidence. This bound is used to select among different model choices that are defined by the number of mesostates as well as by the number of stationary linear regimes. The full model is compared to a simplified version that uses no dynamical assumptions as well as to a standard EEG inversion technique. The comparison is carried out using an extensive set of simulations, and the application of SMSM to a real data set is also demonstrated. Our results show that for experimental situations in which we have some a priori belief that there are multiple approximately linear dynamical regimes, the proposed SMSM provides a natural modelling tool.

Evaluation and calibration of functional network modeling methods based on known anatomical connections

Recent studies have identified large scale brain networks based on the spatio-temporal structure of spontaneous fluctuations in resting-state fMRI data. It is expected that functional connectivity based on resting-state data is reflective of - but not identical to - the underlying anatomical connectivity. However, which functional connectivity analysis methods reliably predict the network structure remains unclear. Here we tested and compared network connectivity analysis methods by applying them to fMRI resting-state time-series obtained from the human visual cortex. The methods evaluated here are those previously tested against simulated data in Smith et al. (Neuroimage, 2011). To this end, we defined regions within retinotopic visual areas V1, V2, and V3 according to their eccentricity in the visual field, delineating central, intermediate, and peripheral eccentricity regions of interest (ROIs). These ROIs served as nodes in the models we study. We based our evaluation on the "ground-truth", thoroughly studied retinotopically-organized anatomical connectivity in the monkey visual cortex. For each evaluated method, we computed the fractional rate of detecting connections known to exist ("c-sensitivity"), while using a threshold of the 95th percentile of the distribution of interaction magnitudes of those connections not expected to exist. Under optimal conditions - including session duration of 68min, a relatively small network consisting of 9 nodes and artifact-free regression of the global effect - each of the top methods predicted the expected connections with 67-85% c-sensitivity. Correlation methods, including Correlation (Corr; 85%), Regularized Inverse Covariance (ICOV; 84%) and Partial Correlation (PCorr; 81%) performed best, followed by Patel's Kappa (80%), Bayesian Network method PC (BayesNet; 77%), General Synchronization measures (67-77%), and Coherence (CohB; 74%). With decreased session duration, these top methods saw decreases in c-sensitivities, achieving 59-76% for 17min sessions. With a short resting-state fMRI scan of 8.5min, none of the methods predicted the real network well, with Corr (65%) performing best. With increased complexity of the network from 9 to 36 nodes, multivariate methods including PCorr and BayesNet saw a decrease in performance. Artifact-free regression of the global effect increased the c-sensitivity of the top-performing methods. In an overall evaluation across all tests we performed, correlation methods (Corr, ICOV, and PCorr), Patel's Kappa, and BayesNet method PC set themselves somewhat above all other methods. We propose that data-based calibration based on known anatomical connections be integrated into future network studies, in order to maximize sensitivity and reduce false positives.